Watson said the agent felt threatened and that his family could not return to the plane until he deleted his tweet.

"Then there's an announcement that comes the overhead announcement system and it said, 'Will the Watson party please gather your belongings and exit the aircraft,'" Watson said.

The family was eventually allowed back on the plane.

Southwest said in a statement that the customer was "briefly removed" from the flight "to resolve the conversation outside of the aircraft and away from the other passengers." The airline, which is investigating the situation, said it has offered Watson "vouchers as a gesture of goodwill."